{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pylab as pl\n",
    "import numpy as np\n",
    "from scipy import integrate\n",
    "from scipy.integrate import odeint\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams['font.sans-serif'] = ['SimHei']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 数值积分-integrate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 球的体积"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def half_circle(x):\n",
    "    return (1-x**2)**0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.1415893269307373"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 10000\n",
    "x = np.linspace(-1, 1, N)\n",
    "dx = x[1] - x[0]\n",
    "y = half_circle(x)\n",
    "2 * dx * np.sum(y) # 面积的两倍 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.1415893269315975"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.trapz(y, x) * 2 # 面积的两倍"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.141592653589797"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import integrate\n",
    "pi_half, err = integrate.quad(half_circle, -1, 1)\n",
    "pi_half * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def half_sphere(x, y):\n",
    "    return (1-x**2-y**2)**0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.094395102393199 1.0002356720661965e-09 2.0943951023931953\n"
     ]
    }
   ],
   "source": [
    "volume, error = integrate.dblquad(half_sphere, -1, 1, \n",
    "        lambda x:-half_circle(x), \n",
    "        lambda x:half_circle(x))\n",
    "\n",
    "print (volume, error, np.pi*4/3/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 解常微分方程组"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18b3f0fc2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%fig=洛伦茨吸引子：微小的初值差别也会显著地影响运动轨迹\n",
    "from scipy.integrate import odeint \n",
    "import numpy as np \n",
    "\n",
    "def lorenz(w, t, p, r, b): #❶\n",
    "    # 给出位置矢量w，和三个参数p, r, b计算出\n",
    "    # dx/dt, dy/dt, dz/dt的值\n",
    "    x, y, z = w.tolist()\n",
    "    # 直接与lorenz的计算公式对应 \n",
    "    return p*(y-x), x*(r-z)-y, x*y-b*z\n",
    "\n",
    "t = np.arange(0, 30, 0.02) # 创建时间点 \n",
    "# 调用ode对lorenz进行求解, 用两个不同的初始值 \n",
    "track1 = odeint(lorenz, (0.0, 1.00, 0.0), t, args=(10.0, 28.0, 3.0)) #❷\n",
    "track2 = odeint(lorenz, (0.0, 1.01, 0.0), t, args=(10.0, 28.0, 3.0)) #❸\n",
    "#%hide\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "fig = pl.figure()\n",
    "ax = Axes3D(fig)\n",
    "ax.plot(track1[:,0], track1[:,1], track1[:,2], lw=1)\n",
    "ax.plot(track2[:,0], track2[:,1], track2[:,2], lw=1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ode类"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mass_spring_damper(xu, t, m, k, b, F):\n",
    "    x, u = xu.tolist()\n",
    "    dx = u\n",
    "    du = (F - k*x - b*u)/m\n",
    "    return dx, du "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18b412006a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%fig=滑块的速度和位移曲线\n",
    "m, b, k, F = 1.0, 10.0, 20.0, 1.0\n",
    "init_status = 0.0, 0.0\n",
    "args = m, k, b, F\n",
    "t = np.arange(0, 2, 0.01)\n",
    "result = odeint(mass_spring_damper, init_status, t, args)\n",
    "#%hide\n",
    "fig, (ax1, ax2) = pl.subplots(2, 1)\n",
    "ax1.plot(t, result[:, 0], label=u\"位移\")\n",
    "ax1.legend()\n",
    "ax2.plot(t, result[:, 1], label=u\"速度\")\n",
    "ax2.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.integrate import ode\n",
    "\n",
    "class MassSpringDamper(object): #❶\n",
    "    \n",
    "    def __init__(self, m, k, b, F):\n",
    "        self.m, self.k, self.b, self.F = m, k, b, F\n",
    "        \n",
    "    def f(self, t, xu):\n",
    "        x, u = xu.tolist()\n",
    "        dx = u\n",
    "        du = (self.F - self.k*x - self.b*u)/self.m\n",
    "        return [dx, du] \n",
    "\n",
    "system = MassSpringDamper(m=m, k=k, b=b, F=F)\n",
    "init_status = 0.0, 0.0\n",
    "dt = 0.01\n",
    "\n",
    "r = ode(system.f) #❷\n",
    "r.set_integrator('vode', method='bdf')\n",
    "r.set_initial_value(init_status, 0)\n",
    "\n",
    "t = []\n",
    "result2 = [init_status]\n",
    "while r.successful() and r.t + dt < 2: #❸\n",
    "    r.integrate(r.t + dt)\n",
    "    t.append(r.t)\n",
    "    result2.append(r.y)\n",
    "    \n",
    "result2 = np.array(result2)\n",
    "np.allclose(result, result2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "class PID(object):\n",
    "    \n",
    "    def __init__(self, kp, ki, kd, dt):\n",
    "        self.kp, self.ki, self.kd, self.dt = kp, ki, kd, dt\n",
    "        self.last_error = None\n",
    "        self.status = 0.0\n",
    "        \n",
    "    def update(self, error):\n",
    "        p = self.kp * error\n",
    "        i = self.ki * self.status\n",
    "        if self.last_error is None:\n",
    "            d = 0.0\n",
    "        else:\n",
    "            d = self.kd * (error - self.last_error) / self.dt\n",
    "        self.status += error * self.dt\n",
    "        self.last_error = error\n",
    "        return p + i + d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "控制力的终值: 19.943404699515057\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x18b42591cc0>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18b4150b9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%fig=使用PID控制器让滑块停在位移为1.0处\n",
    "def pid_control_system(kp, ki, kd, dt, target=1.0):\n",
    "    system = MassSpringDamper(m=m, k=k, b=b, F=0.0)\n",
    "    pid = PID(kp, ki, kd, dt)\n",
    "    init_status = 0.0, 0.0\n",
    "\n",
    "    r = ode(system.f)\n",
    "    r.set_integrator('vode', method='bdf')\n",
    "    r.set_initial_value(init_status, 0)\n",
    "\n",
    "    t = [0]\n",
    "    result = [init_status]\n",
    "    F_arr = [0]\n",
    "\n",
    "    while r.successful() and r.t + dt < 2.0:\n",
    "        r.integrate(r.t + dt)\n",
    "        err = target - r.y[0]  #❶\n",
    "        F = pid.update(err)  #❷\n",
    "        system.F = F  #❸\n",
    "        t.append(r.t)\n",
    "        result.append(r.y)\n",
    "        F_arr.append(F)\n",
    "\n",
    "    result = np.array(result)\n",
    "    t = np.array(t)\n",
    "    F_arr = np.array(F_arr)\n",
    "    return t, F_arr, result\n",
    "\n",
    "\n",
    "t, F_arr, result = pid_control_system(50.0, 100.0, 10.0, 0.001)\n",
    "print(u\"控制力的终值:\", F_arr[-1])\n",
    "#%hide\n",
    "fig, (ax1, ax2, ax3) = pl.subplots(3, 1, figsize=(6, 6))\n",
    "ax1.plot(t, result[:, 0], label=u\"位移\")\n",
    "ax1.legend(loc=\"best\")\n",
    "ax2.plot(t, result[:, 1], label=u\"速度\")\n",
    "ax2.legend(loc=\"best\")\n",
    "ax3.plot(t, F_arr, label=u\"控制力\")\n",
    "ax3.legend(loc=\"best\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\optimize\\_basinhopping.py:282: OptimizeWarning: Unknown solver options: approx_grad\n",
      "  return self.minimizer(self.func, x0, **self.kwargs)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[56.67106149 99.97434757  1.33963577]\n",
      "Wall time: 55.1 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "from scipy import optimize\n",
    "\n",
    "\n",
    "def eval_func(k):\n",
    "    kp, ki, kd = k\n",
    "    t, F_arr, result = pid_control_system(kp, ki, kd, 0.01)\n",
    "    return np.sum(np.abs(result[:, 0] - 1.0))\n",
    "\n",
    "\n",
    "kwargs = {\n",
    "    \"method\": \"L-BFGS-B\",\n",
    "    \"bounds\": [(10, 200), (10, 100), (1, 100)],\n",
    "    \"options\": {\n",
    "        \"approx_grad\": True\n",
    "    }\n",
    "}\n",
    "\n",
    "opt_k = optimize.basinhopping(\n",
    "    eval_func, (10, 10, 10), niter=10, minimizer_kwargs=kwargs)\n",
    "print(opt_k.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t=0.5000000000000002, x=1.07098, u=0.315352\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18b2fb52400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%fig=优化PID的参数降低控制响应时间\n",
    "kp, ki, kd = opt_k.x\n",
    "t, F_arr, result = pid_control_system(kp, ki, kd, 0.01)\n",
    "idx = np.argmin(np.abs(t - 0.5))\n",
    "x, u = result[idx]\n",
    "print (\"t={}, x={:g}, u={:g}\".format(t[idx], x, u))\n",
    "#%hide\n",
    "fig, (ax1, ax2, ax3) = pl.subplots(3, 1, figsize=(6, 6))\n",
    "ax1.plot(t, result[:, 0], label=u\"位移\")\n",
    "ax1.legend(loc=\"best\")\n",
    "ax2.plot(t, result[:, 1], label=u\"速度\")\n",
    "ax2.legend(loc=\"best\")\n",
    "ax3.plot(t, F_arr, label=u\"控制力\")\n",
    "ax3.legend(loc=\"best\");"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
